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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A transformation for an $n$-balanced $_ 3\Phi _ 2$
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by H. M. Srivastava PDF
Proc. Amer. Math. Soc. 101 (1987), 108-112 Request permission

Abstract:

An interesting generalization of the familiar $q$-extension of the Pfaff-Saalschütz theorem is proved and is applied, for example, to derive a reduction formula for a certain double $q$-series. The main theorem (asserting the symmetry in $n$ and $N$ of a function $f(n,N)$ defined in terms of an $n$-balanced basic (or $q{\text { - }}$-) hypergeometric $_3{\Phi _2}$ series by equation (8)) is essentially a $q$-extension of Sheppard’s transformation.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 101 (1987), 108-112
  • MSC: Primary 33A30; Secondary 05A30
  • DOI: https://doi.org/10.1090/S0002-9939-1987-0897079-3
  • MathSciNet review: 897079